A spherical pendulum consists of a bob of mass m attached to a weightless, extension less rod of length l. The end of the rod opposite the bob pivots freely (in all directions) about some fixed point. Set up the Hamiltonian function in spherical coordinates. (If PФ = 0, the result is the same as that for the plane pendulum.) Combine the term that depends on PФ with the ordinary potential energy term to define as effective potential V(θ, PФ). Sketch V as a function of θ for several values of PФ, including PФ = 0. Discuss the features of the motion, pointing out the differences between PФ = 0 and PФ ≠ 0. Discuss the limiting case of the conical pendulum (θ = constant) with reference to the V-θ diagram.